Based on the classical elasto-plastic theory, the transformed stress space deduced from the spatially mobilized plane(SMP) criterion and a new concept of similar elastic volume modulus, the stress-strain incremental equations of soils for the asymptotic state constitutive model were established. A simple stress-strain incremental matrix under triaxial compression condition was formulated, in which the modified Cam-clay model was a special case. The stress-strain incremental equations were then proposed to simulate the stress-strain relationships in some triaxial stress path tests as the triaxial compression, the consolidated undrained and the strain incremental ratio controlled. The proposed equations were used to simulate and compare the triaxial test results. They show that the equations proposed can be used easily and the asymptote state model can describe the stress-strain and strength behaviors of soils reasonably.